The singular-value decomposition in the extended max algebra Original Research Article

First we establish a connection between the field of the real numbers and the extended max algebra, based on asymptotic equivalences. Next we propose a further extension of the extended max algebra that will correspond to the field of the complex numbers. Finally we use the analogy between the field of the real numbers and the extended max algebra to define the singular-value decomposition of a matrix in the extended max algebra and to prove its existence.